Application of the variational iteration method for nonlinear free vibration of conservative oscillators

In this paper, an analytical solution for the nonlinear free vibration of a conservative oscillatoris presented. the nonlinear governing equation is solved by employing the variational iteration method(vim). this method is based on the use of lagrange multipliers for identification of optimal values ofparameters in a function. obtained results reveal that the proposed method is very effective, simple andexact. in the present investigation, the results of this method are compared with those of the homotopyanalysis method (ham), as well as those predicted by the rungekutta method. the excellent accuracy ofthe obtained results is demonstrated by comparing them with available analytical and numerical resultsavailable in the literature. furthermore, the numerical results for different particular cases of the problemare presented. the effects of different parameters on the ratio of nonlinear to linear natural frequency ofthe system are also studied. consequently, the proposed analytical solution can be used as an efficienttool to study the effects of the material or geometrical parameters in the modeling of devices consistingof nonlinear conservative oscillators for their design and optimization, which requires a large number ofsimulations.